Real time gamma-ray signature identifier

ABSTRACT

A real time gamma-ray signature/source identification method and system using principal components analysis (PCA) for transforming and substantially reducing one or more comprehensive spectral libraries of nuclear materials types and configurations into a corresponding concise representation/signature(s) representing and indexing each individual predetermined spectrum in principal component (PC) space, wherein an unknown gamma-ray signature may be compared against the representative signature to find a match or at least characterize the unknown signature from among all the entries in the library with a single regression or simple projection into the PC space, so as to substantially reduce processing time and computing resources and enable real-time characterization and/or identification.

I. CLAIM OF PRIORITY IN PROVISIONAL APPLICATION

This application claims the benefit of U.S. provisional application No.60/665,619 filed Mar. 25, 2005, entitled, “Real Time Gamma-Ray SignatureIdentifier” by Mark S. Rowland et al.

The United States Government has rights in this invention pursuant toContract No. W-7405-ENG-48 between the United States Department ofEnergy and the University of California for the operation of LawrenceLivermore National Laboratory.

II. FIELD OF THE INVENTION

The present invention relates to gamma-ray signature/sourceidentification methods. More particularly, the invention relates to areal time, non-processor intensive, gamma-ray signature/sourceidentification method and system using a transformed and minimizedsignature of a large comprehensive spectral library to find a match orat least characterize an unknown signature from among all entries of thelibrary without having to compare/fit the unknown against each entry.

III. BACKGROUND OF THE INVENTION

Identification of nuclides measured by gamma-ray spectrometry istypically performed by focusing on the peaks of an unknown spectrum, andin particular by curve-fitting the peaks to a library ofknown/predetermined spectral signatures. For example, peak energyassignments are made to nuclides (isotopes), and regression is used tocompare pre-determined measurements or calculated spectra to an unknown.Using only peaks, however, can be limiting because information usefulfor identification may also be found elsewhere in the continuum of thefull spectrum. For example, Compton scattering of some gamma-rays causescount data to spread beyond the peak locations to the continuum. ThisCompton scattered part of the gamma-ray spectrum contains informationabout the radioactive source and the gamma-ray detector. Furthermore,shielded sources frequently contain more counts in the continuum than inthe peaks, making identification difficult. For example, peaks tend tovanish when shielding is thick.

Ideally therefore, all available information, including both peaks andcontinuum, would be used in a comprehensive analysis called “fullspectrum analysis” to best determine the identity of an unknown sourcewithout requiring prior knowledge of any shielding. Automating fullspectrum analysis to run unattended on a computer, however, has been achallenge because of both a limited ability to model or measure all therelevant physics for all possible sources and shields, and the processorintensive nature of comparing an unknown spectrum against all entries ina given spectral library.

A typical example of full spectrum analysis and gamma-ray signatureidentification in the prior art involves first creating a library ofpossible signatures, such as by measuring known signatures, calculatingknown signatures in real time, or pre-calculating known signatures for acatalog. Multiple regression is then performed to search for the mostsimilar match of an unknown to a known in the library, where the testfor similarity may be a test for maximum likelihood, chi-square orsimple differences. Regression test comparison involves solving a linearseries of equations, usually reduced to array algebra, typically where amatrix is inverted. Matrix inversion can become unreliable as libraryelements become similar. And since computer time is proportional to thenumber of channels (energy increments) in the gamma-ray spectrum timesthe number of library elements, providing a large library cansignificantly increase processing time/computing resources. For example,8000 library elements times 200 channels is 1.6 million operations.Furthermore, fine tuning the library at regression time is anotheroption known in the art, where the calculation codes generate newvariations as the regression is running. This approach, however, cantake even longer since computational time is proportional to the numberof channels in the spectrum times the number of library elements timesthe number of seconds to calculate a spectral variation.

Since the possible list of predetermined known entries for whichvariations must be calculated is typically in the hundreds, and not thetypical range of up to about thirty predetermined known entries in thelibrary that exist in commercial algorithms, this pushes a typicalmultiple regression or regression/model approach to take up to hours ofCPU time, especially if geometry variational calculations are involved.Because of these limitations, traditional regression approachestypically have limited library sizes in order to reduce the total numberof regressions performed and keep CPU time reasonable. The disadvantageof small libraries, however, is that they induce classically systematicerrors leading to incorrect library lookup. As a consequence, theresults of such an identification scheme using a limited library may notprovide a complete or accurate characterization or identification of theunknown spectrum.

What is needed therefore is a real-time (i.e. on the order of a secondor less) method and system for identifying gamma-ray signatures thatuses little computer processor time and resources, analyzes the fullgamma-ray spectrum, and can be adjusted to address numerousidentification objectives, such as for example nuclide ID, sourcestrength, age, shielding thickness, or nuclear material form. Inparticular, what is needed is a method and system that effectivelytransforms and reduces the voluminous spectral data contained in acomprehensive spectral library to a small, manageablerepresentation/signature(s) of the library, and directly compares anunknown spectrum against the representation(s) to find a match or atleast determine a characterization of the unknown by similarity to allspectral entries of the library. Moreover, this is performed without thecomputational burden of having to perform fine-grain multipleregression, i.e. fitting the unknown against each entry of the sourcelibrary. Additionally, and with respect to building the library, such amethod and system would also be configured to obtain factualinformation/details about the signatures used as library entries,without having to particularly measure for the information. While suchinformation is typically obtained by measurement, it would beadvantageous to instead use suitably accurate simulations of theknown/predetermined signatures to obtain this information and therebyavoid the expense (in terms of processor time/computing resources)associated with actually measuring for all possible variations on thesignatures when building a comprehensive library.

IV. SUMMARY OF THE INVENTION

One aspect of the present invention includes a real time gamma-raysignature/source identification method using principal componentsanalysis (PCA) for transforming and substantially reducing one or morecomprehensive spectral libraries of nuclear materials types andconfigurations into at least one corresponding conciserepresentation/signatures(s) representing and indexing each individualpredetermined spectrum in the principal component (PC) space, wherein anunknown gamma-ray signature may be compared against the one or morerepresentative signature(s) to find a match or at least characterize theunknown signature from among all the entries in the library with asingle regression or simple projection into the PC space per signature,so as to substantially reduce processing time and computing resourcesand enable real-time characterization and/or identification.

Another aspect of the present invention includes a real-time method ofidentifying radioactive materials by their gamma-ray signaturescomprising: providing at least one library of predetermined spectra forvarious nuclear material types; performing principal component analysison the library to produce a corresponding transformed basis setrepresenting the library and indexing each spectrum of the library inprincipal component space; projecting an unknown spectrum onto theprincipal component space; and determining the identity of the unknownspectrum by its proximity to clusters of the basis set in the principalcomponent space.

Another aspect of the present invention includes a real-timecomputerized gamma-ray signature identification system comprising: atleast one library of predetermined spectra for various nuclear materialtypes and configurations; computer processor means for performingprincipal component analysis on the library to transform the libraryinto a corresponding basis set representing the library and indexingeach spectrum of the library in principal component space; computerprocessor means for determining the identity of the unknown spectrum byprojecting an unknown spectrum onto the principal component space anddetermining its proximity to clusters of the basis set in the principalcomponent space.

Another aspect of the present invention includes a real-timecomputerized gamma-ray signature identification system comprising: atleast one library of predetermined spectra for various nuclear materialtypes and configurations; a principal component analysis module adaptedto perform principal component analysis on the library so as totransform the library into a basis set representing the library andindexing each spectrum of the library in principal component space; aninput module for receiving an unknown spectrum to be identified; andcomputer processor means for determining the identity of the unknownspectrum by projecting the unknown spectrum onto the principal componentspace and determining its proximity to clusters of the basis set in theprincipal component space.

Another aspect of the present invention includes an article ofmanufacture comprising: a computer usable medium having computerreadable program code means embodied therein for identifying inreal-time radioactive materials by their gamma-ray signatures, thecomputer readable program code means comprising: at least one computerreadable library of predetermined spectra for various nuclear materialtypes; computer readable program code means for performing principalcomponent analysis on the library to produce a transformed basis setrepresenting the library and indexing each spectrum of the library inprincipal component space; computer readable program code means fordetermining the identity of the unknown spectrum by projecting anunknown spectrum onto the principal component space and determining itsproximity to clusters of the basis set in the principal component space.

Generally, the method of the present invention proceeds by modeling ormeasuring with all the fidelity necessary to capture all the informationtheoretically present in a detector signature and collecting in acomprehensive, large literal library. The maximum information contentmostly relates to the resolution properties of the gamma-rayspectrometer. With respect to library creation, the method need not relyon calculations to include all the necessary detail (i.e. it is notbound by empirical limitations), but may rather enable the extraction ofthe available information from the measuring system. Thusresolution-limited information content drives and determines thesensibility limits on how many things would be calculated to add to andenhance the library.

PCA is then performed to condense the large library to one or morecompact representative signature(s) of attributes (i.e. principalcomponents), each typically comprising 5 to 20 orthogonal descriptors.Fast comparison is possible because one lookup gives a match. The largelibrary is further enhanced to characterize all variations. Inparticular, PCA labeling, unitization, subsets, and/or energy bin-setsare used to derive, find, or otherwise characterize different kinds ofinformation.

An unknown measurement/spectrum is then converted into PCA coordinatespace. This involves a single, simple operation to get PC coordinatesper signature which may be accomplished in several ways. For example,conversion can be performed most easily with a single regression of thePC's chosen (typically 5 to 20) with the unknown spectrum. Amplitudes ofthe PC's that optimally match the data are the coordinates.

Then, proximity determination is performed to lookup the nearestneighbors in the library, i.e. closest to the coordinates of theunknown. This is a single sort which is fast on a computer and wherecomputer time is proportional to n times m where n is the length of thelist and m is the number of selected PC's. For example, with 8000library elements times and the number of selected PC's being <20 thecomputer time is about 160000 operations, or about 10 times faster thana regression approach. Reporting information is stored along with thecoordinates, and may be varied in complexity to suit different userneeds, and is presented with the nearest neighbor found. Answer qualityhas the merit of being thorough, because the library may be big, andbecause the PC's are selected to intentionally represent all theinformation present in the data that a spectrometer provides.

The following is a general outline of the method steps of a preferredembodiment of the present invention:

(1) Create models in measurement space

-   -   model alteration options        -   add background model, or        -   don't add background

(2) Make PCA library

-   -   transform library to coordinate space and catalog        -   unitize the magnitude, or        -   leave the magnitude scale absolute

(3) Search for similarity in the first library

-   -   subtract background, or not, depending on type of library        created    -   transform unknown to the above library coordinate space    -   lookup nearest neighbors    -   conditional test to decide if and which library might next be        searched.

(4) Search for similarity in the second library

-   -   subtract background, or not, depending on type of library        created    -   transform unknown to the above library coordinate space    -   lookup nearest neighbors    -   conditional test to decide if and which library might next be        searched.

(5) Search more libraries search if desired

(6) Combine results from steps (3) through (5).

V. BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated into and form a partof the disclosure, are as follows.

FIG. 1 is a schematic flow diagram illustrating the method steps of apreferred embodiment of the present invention.

VI. DETAILED DESCRIPTION

The present invention is generally directed to a gamma-ray signatureidentification method and system by full spectrum analysis, usingprincipal component analysis (PCA) to substantially compress or reduceone or more analytically comprehensive libraries of modeled, tabulatedor otherwise predetermined spectra into a corresponding small basisset(s). The basis set is a transformed and minimized representation ofall spectra in the library, and is used instead of the library entriesfor fitting and identifying an unknown spectrum. Moreover, the use ofthe basis set enables the identification of the unknown spectrum with asingle regression/simple projection, and avoids the multiple regressionsrequired in the prior art when comparing against each spectrum in alibrary. One advantage of this arrangement is that it substantiallyreduces the processing time and computing resources necessary to performthe identification against an existing library. It also substantiallyreduces the processing time necessary to additionally calculate inreal-time (i.e. while the next increment of data is collected or withinthe time it took to make the measurement) the shielding variations.Furthermore, it enables the creation and use of an expanded,comprehensive spectral library including substantially all nuclearmaterial types, including intrinsic and extrinsic variations, such asshielding configurations, which was otherwise not possible due to theprocessor intensive nature of fitting an unknown spectrum against allspectra in a library.

It is appreciated that PCA is generally an exploratory multivariatestatistical technique known in the art that allows the identification ofkey variables (or combinations of variables) in a multi-dimensional dataset that best explain the differences between observations. PCAtransforms a multivariate data set in such a manner that only a few ofthe new, uncorrelated varieties (PC's) are needed to retain nearly allof the variation present in the original data set. Given m observationson n variables, PCA serves to reduce the dimensionality of the datamatrix by finding r new variables (r≦n). These r PC's account togetherfor as much of the variance in the original n variables as possiblewhile remaining mutually uncorrelated and orthogonal. In this manner thefirst few PC's may be used as a multi-component signature that iscapable of describing the feature space of expected gamma-radiationsignatures with considerable accuracy. Thus PCA serves to reducedimensionality while filtering noise in the process, making the datamore accessible for visualization and analysis.

Implementation of PCA for gamma-ray source identification in the presentinvention includes the following steps: (1) preparation of one or morelibraries of gamma-ray spectra that samples the gamma-ray source spaceof interest, (2) PCA is performed on the spectral library(s) and (3)unknown spectrum is projected into the PC space and the known sourcetypes/configurations which are closest distancewise to the unknown areidentified as most consistent with the unknown, wherein distance issimilarity or Curies or inches of shielding or nuclide identity. FIG. 1shows an exemplary flow scheme of the present invention.

In FIG. 1, reference character 10 shows a first step where models arefirst created in measurement space to produce at least one largespectral library. Preparation of the comprehensive source library isaccomplished by first modeling/measuring and tabulating Photo-peak,Compton, escape and secondary peak signatures to identify source types,e.g. simple sources such as 57 Co, parent-daughter mixtures such as99Mo/99m Tc, varieties of heavy element sources such as weapons-grade orreactor-grade plutonium, etc. Intrinsic and extrinsic variations on thesources are also identified and included in the library. Intrinsicvariations may include, for example, time elapsed since chemicalseparation. And extrinsic variations may include, for example, packagingor other intervening material types/configurations (e.g. shieldingconfigurations) that will alter the gamma-ray spectra of the sourcetypes. (See below for greater discussion of creating variations in thelibrary) The many various combinations of these variations are used tocreate comprehensive source libraries comprising many thousands ofgamma-ray spectra.

While spectral information is typically obtained by measurement, it mayalternatively be obtained using suitably accurate simulations of theknown/predetermined signatures and thereby avoid the expense (in termsof processor time/computing resources) associated with actuallymeasuring for all possible variations on the signatures when building acomprehensive library. To this end, an algorithm may be utilized that,with enough fidelity, can calculate all signature variations to avoidthe difficulty of measuring everything. The spectra used as entries forthe library may be obtained, for example using an automation script thatdescribes each of the source variations desired and runs the spectrumgenerator. For example, a widely available radiation transport code,such as MCNP (copyright UC-LANL), may be used to compute the largelibrary of spectra, including detector response features. The scriptwould command a combined radiation transport/instrument responsecomputer calculation that computes library elements. An alternative tocalculating libraries is to measure the library elements. This wouldinvolve obtaining all radioactive sources, with varying strengths, manythicknesses of shielding material and types, and then every detector tomeasure all possible combinations of source, shielding, and detector.

It is appreciated that when collecting the spectral data for preparingthe library, the spectra may be formatted, unitized, or otherwisepre-processed to produce different model groups (i.e. multiplelibraries) and facilitate subsequent processing and comparison tounknown spectra. For example, in the case of unitizing the originaldata, all spectra models in the library may be scaled or normalized to,say 100 counts, to remove variations in source strength. Formulating alibrary in this manner forces the algorithmic approach of the presentinvention to focus on identifying the nuclide, as opposed to the sourcestrength. This makes possible the running of both a unitized and anon-unitized library, after which combining the results gives moreinsight into the nature of an unknown source. Thus, another aspect toformulating the libraries is that the approach of the present inventionincludes the ability to commingle measurements and simulations. It isanticipated that an end user will want to include unique measurements,outliers, etc. in the PCA library of computed spectra. The algorithmicapproach of the present invention to spectral ID (using PCA) specifiesthat the library may be in measurement space and therefore accepts theaddition of a library element derived through means other thancalculation.

It is also notable that the spectral models may be grouped (overlappingor not) to produce one or more libraries comprising spectral families,categories, and/or sub-categories which share common characteristics.For example, a main library may be a generic list containing the spectraof all models, while another library may be specific to special nuclearmaterials (SNM), and thereby provide greater insight into the nature ofthe unknown spectrum. Inherent in the lookup of the closest match to anunknown, is the labeling of the library element. It may be simplycalled, for example, Nuclide-X, or “Bad-Nuclide”, where the choice istherefore based on the end-user needs for information. Different levelsof information are easily defined with the library elements for thepurpose of imparting the correct information.

PCA is next performed on the spectral library(s), as indicated atreference character 11 in FIG. 2, to decompose the tabulated results ofthe original spectral data set into a corresponding small basis setwhich is a projection of the original spectral data into principalcomponent (PC) space. Thus the basis set is a transformed and minimizedrepresentation of the library that can index and describe any tabulatedresult with a linear combination of basis vectors (i.e. principalcomponents). In the process of making the PC's, one selects a subset ofthe PC's, such that the variance present in the library is addressed bythe subset of PC's. This may be provided by a user who inputs the numberof PC's to be used. This may result in the library variations beingaddressed to, for example, the 98^(th) percentile. Selecting fewer PC'swill run faster, but describe less of the variance. For low resolutiondetectors, the information content in the library presents degeneracies.These degeneracies are situations where there is no apparent differencebetween two measurements or library elements. Since this is the realitywith all low resolution detectors, there will be a maximum number ofPC's necessary to identify the information present in an unknowngamma-ray spectrum. As spectrometer resolution decreases (i.e. NaI toplastic), fewer PC's are necessary to describe the information that ispresent in an unknown spectrum. Non-unitized large libraries may be wellrepresented by as few as four PC's. It is appreciated that PCA may beapplied to each library where multiple categorical libraries areprovided, to generate corresponding basis sets. In this manner, theidentification inquiry of an unknown spectrum may be tailored toparticular libraries in order to answer user-specific questions of theunknown spectrum and achieve greater insight into the nature, character,and identity thereof. In effect, the provision of multiple librariesserves to reduce even more dimensions of variance and complexityaccomplished by PCA.

It can be appreciated that one beneficial attribute to the PCA approachis that proximity (as in a non-exact library lookup match) relates tothe feature errors in the model. For example, given two sources in thelibrary, one with shielding and the other without, if the unknownsignature has half shielding its coordinates are half way between thetwo library elements. Its nearest neighbors are identified and thedistances to each are provided, allowing an interpolation of a thicknessfor the shield. Since much of the prior art operates with 30 elementsand interpolate with regression (limited), whereas the present inventionputs all identified unknowns in the library, the present invention isexpected to have at least 5 times more depth of spectrumcharacterization. While doing more is possible, there is a point ofdiminishing return driven by the limited information content in lowresolution detectors. Thus the algorithm of the present invention servesto calculate all signature variations using suitably accuratesimulations to avoid the difficulty of actually measuring every possiblevariation.

One exemplary method of implementing PCA involves using a PCAcode/software which first locates a rebinning file to a file of energybin limits and rebins each spectrum in the gamma-ray spectrum libraryinto a smaller, more manageable number of bins, such as 100-300.Following rebinning, the PCA is performed. For this step, a user mayprovide input as to the number of principal components (PC's) to be usedfor PCA analysis. The results of the analysis are saved to a data fileand include the PC's and the PC scores (i.e. the location of the eachindividual spectrum for the library in the PC space, and labelattributes that describe the salient nature of each library element.

Identification is performed by projecting the unknown into PC space.Implementation of the identification step may be accomplished, forexample, using a computer code is run that allows the user to input anunknown spectrum. The input step is shown at reference character 12 ofFIG. 1. The specified energy bin set (if used) is used with a particularPCA library, and the desired number of PC's to be used for analysis. Asshown at 13, the unknown is then rebinned (if needed), normalized (ifneeded), and rotated into the PC space, i.e. the unknown spectrum isprojected into the space described by the basis set that was derivedfrom all the library models. The rotation is the regression to get PCamplitudes.

Similarity to library models is next measured (at 14 in FIG. 1) by theproximity to nearby library models in the PC space described by thebasis set, with the Mahalanobis distance used as the proximity measure.The proximity to and the character of the nearby cluster of modelsrepresent a statement of identity which is translated into specificcharacteristics that describe the unknown. In particular, theMahalanobis distances are sorted by increasing value with the lowestvalues being most consistent, and therefore the source associated withthat PC score being most consistent, with the item producing theMahalanobis distance. The Mahalanobis distance is used for interpolatingattribute dimensions in library sets assembled for the purpose ofinterpolating, thereby increasing the range of library coverage.

As previously mentioned, various identification objectives may be met bytailoring the contents in a library of models, by running differentlibraries sequentially, and/or building a logic sequence for formingconclusions based on intermediate analysis results. This is shown atreference characters 15 and 16 in FIG. 1. An example of runningsequential libraries is to run the unitized set first to get the ID,then run a non-unitized set with only that nuclide but with sourcestrength variations. Logical conclusions may be constructed, forexample, by noting that SNM may not be close to the unknown in theunitized library lookup, but by secondarily running the unknown throughthe SNM only library, one may construct a conditional probability suchas “while most likely the unknown is nuclide-X, if SNM were present inhidden form, it would most likely be SNM-Y. At step 17, the results fromall similarity searches are then combined. It is appreciated that whilea computer program is discussed for implementing the present invention,the implementation of the functions described herein may be accomplishedequally by, for example, hardware, firmware, IC, etc. specificallydesigned with such functionalities.

While particular operational sequences, materials, temperatures,parameters, and/or particular embodiments have been described and orillustrated, such are not intended to be limiting. Modifications andchanges may become apparent to those skilled in the art, and it isintended that the invention be limited only by the scope of the appendedclaims.

1. A real-time method of identifying radioactive materials by theirgamma-ray signatures comprising: providing at least one library ofpredetermined spectra for various nuclear material types; performingprincipal component analysis on the library to produce a correspondingtransformed basis set representing the library and indexing eachspectrum of the library in principal component space; projecting anunknown spectrum onto the principal component space; and determining theidentity of the unknown spectrum by its proximity to clusters of thebasis set in the principal component space.
 2. The real-timecomputerized gamma-ray signature identification system of claim 1,wherein the step of providing the library of predetermined spectraincludes calculating signature variations to avoid the difficulty ofmeasuring for signature variations.
 3. The real-time computerizedgamma-ray signature identification system of claim 1, wherein thelibrary includes predetermined spectra for various nuclear materialtypes and associated intrinsic and extrinsic variations.
 4. Thereal-time computerized gamma-ray signature identification system ofclaim 3, wherein the extrinsic variations include shieldingconfigurations.
 5. The real-time computerized gamma-ray signatureidentification system of claim 1, wherein the library is a comprehensivelibrary having entries representing substantially more than thirty (e.g.hundreds or thousands) spectral models.
 6. The real-time computerizedgamma-ray signature identification system of claim 1, further comprisingunitizing the spectral entries in the library for performing PCA.
 7. Thereal-time computerized gamma-ray signature identification system ofclaim 1, wherein multiple libraries are provided with each havingsub-categorized spectral entries.
 8. The real-time computerizedgamma-ray signature identification system of claim 1, wherein performingPCA includes receiving input for the number of principal components tobe used for PCA.
 9. The real-time computerized gamma-ray signatureidentification system of claim 1, wherein the basis set indexesindividual spectra of the library in the PC space by means of principalcomponent scores.
 10. The real-time computerized gamma-ray signatureidentification system of claim 1, wherein the step of determining theidentity of the unknown spectrum by its proximity to clusters of thebasis set in the principal component space includes the determination ofMahalanobis distances to nearby cluster of models.
 11. A real-timecomputerized gamma-ray signature identification system comprising: atleast one library of predetermined spectra for various nuclear materialtypes and configurations; computer processor means for performingprincipal component analysis on the library to transform the libraryinto a corresponding basis set representing the library and indexingeach spectrum of the library in principal component space; computerprocessor means for determining the identity of the unknown spectrum byprojecting an unknown spectrum onto the principal component space anddetermining its proximity to clusters of the basis set in the principalcomponent space.
 12. A real-time computerized gamma-ray signatureidentification system comprising: at least one library of predeterminedspectra for various nuclear material types and configurations; aprincipal component analysis module adapted to perform principalcomponent analysis on the library so as to transform the library into abasis set representing the library and indexing each spectrum of thelibrary in principal component space; an input module for receiving anunknown spectrum to be identified; and computer processor means fordetermining the identity of the unknown spectrum by projecting theunknown spectrum onto the principal component space and determining itsproximity to clusters of the basis set in the principal component space.13. An article of manufacture comprising: a computer usable mediumhaving computer readable program code means embodied therein foridentifying in real-time radioactive materials by their gamma-raysignatures, the computer readable program code means comprising: atleast one computer readable library of predetermined spectra for variousnuclear material types; computer readable program code means forperforming principal component analysis on the library to produce atransformed basis set representing the library and indexing eachspectrum of the library in principal component space; computer readableprogram code means for determining the identity of the unknown spectrumby projecting an unknown spectrum onto the principal component space anddetermining its proximity to clusters of the basis set in the principalcomponent space.